This document discusses determining whether two lines, m and n, are parallel based on given angle measurements. For the first example, where m∠2 = 123° and m∠8 = 57°, the angles are exterior angles on the same side of the transversal, which must be supplementary for the lines to be parallel. Since m∠2 + m∠8 = 180°, the lines m and n are parallel. For the second example, where m∠3 = 100° and m∠6 = 80°, the angles are alternate interior angles, which must be congruent for the lines to be parallel. But m∠3 ≠ m∠6, so lines m and n are not

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
a) 𝑚∠2 = 123 𝑜
, 𝑚∠8 = 57 𝑜

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
a) 𝑚∠2 = 123 𝑜
, 𝑚∠8 = 57 𝑜
First, what type of angles are ∠2 and ∠8?

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
a) 𝑚∠2 = 123 𝑜
, 𝑚∠8 = 57 𝑜
First, what type of angles are ∠2 and ∠8?
They are exterior angles on the same side of the transversal.

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
a) 𝑚∠2 = 123 𝑜
, 𝑚∠8 = 57 𝑜
First, what type of angles are ∠2 and ∠8?
They are exterior angles on the same side of the transversal.
Exterior angles on the same side of the transversal must be
supplementary for the lines forming them to be parallel.

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
a) 𝑚∠2 = 123 𝑜
, 𝑚∠8 = 57 𝑜
First, what type of angles are ∠2 and ∠8?
They are exterior angles on the same side of the transversal.
Exterior angles on the same side of the transversal must be
supplementary for the lines forming them to be parallel.
So does
𝑚∠2 + 𝑚∠8 = 180 𝑜 ?

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
a) 𝑚∠2 = 123 𝑜
, 𝑚∠8 = 57 𝑜
First, what type of angles are ∠2 and ∠8?
They are exterior angles on the same side of the transversal.
Exterior angles on the same side of the transversal must be
supplementary for the lines forming them to be parallel.
So does
𝑚∠2 + 𝑚∠8 = 180 𝑜 ?
Yes! Therefore, 𝑚||𝑛.

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
b) 𝑚∠3 = 100 𝑜
, 𝑚∠6 = 80 𝑜

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
b) 𝑚∠3 = 100 𝑜
, 𝑚∠6 = 80 𝑜
First, what type of angles are ∠3 and ∠6?

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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
b) 𝑚∠3 = 100 𝑜
, 𝑚∠6 = 80 𝑜
First, what type of angles are ∠3 and ∠6?
They are alternate interior angles.

10. 1
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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
b) 𝑚∠3 = 100 𝑜
, 𝑚∠6 = 80 𝑜
First, what type of angles are ∠3 and ∠6?
They are alternate interior angles.
Alternate interior angles must be congruent for the lines
forming them to be parallel.

11. 1
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m
n
t
Example: Determine whether m must be parallel to n under
the given conditions:
b) 𝑚∠3 = 100 𝑜
, 𝑚∠6 = 80 𝑜
First, what type of angles are ∠3 and ∠6?
They are alternate interior angles.
Alternate interior angles must be congruent for the lines
forming them to be parallel.
𝑚∠3 ≠ 𝑚∠6
Therefore, lines m and n are not parallel.